Improved approximation algorithms for weighted 2-path partitions

Amotz Bar-Noy; David Peleg; George Rabanca; Ivo Vigan

doi:10.1007/978-3-662-48350-3_79

Improved approximation algorithms for weighted 2-path partitions

Amotz Bar-Noy, David Peleg, George Rabanca, Ivo Vigan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

We investigate two NP-complete vertex partition problems on edge weighted complete graphs with 3k vertices. The first problem asks to partition the graph into k vertex disjoint paths of length 2 (referred to as 2-paths) such that the total weight of the paths is maximized. We present a cubic time approximation algorithm that computes a 2-path partition whose total weight is at least .5833 of the weight of an optimal partition; improving upon the (.5265 – ϵ)-approximation algorithm of [26]. Restricting the input graph to have edge weights in {0, 1}, we present a .75 approximation algorithm improving upon the .55-approximation algorithm of [16]. Combining this algorithm with a previously known approximation algorithm for the 3-Set Packing problem, we obtain a .6-approximation algorithm for the problem of partitioning a {0, 1}-edge-weighted graph into k vertex disjoint triangles of maximum total weight. The best known approximation algorithm for general weights achieves an approximation ratio of .5257 [4].

Original language	English
Title of host publication	Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings
Editors	Nikhil Bansal, Irene Finocchi
Publisher	Springer Verlag
Pages	953-964
Number of pages	12
ISBN (Print)	9783662483497
DOIs	https://doi.org/10.1007/978-3-662-48350-3_79
State	Published - 2015
Externally published	Yes
Event	23rd European Symposium on Algorithms, ESA 2015 - Patras, Greece Duration: 14 Sep 2015 → 16 Sep 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9294
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	23rd European Symposium on Algorithms, ESA 2015
Country/Territory	Greece
City	Patras
Period	14/09/15 → 16/09/15

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

Funding

This work is supported by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-09-2-0053, The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation here on.

Funders	Funder number
U.S. Army Research Laboratory
Army Research Laboratory	W911NF-09-2-0053

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10.1007/978-3-662-48350-3_79

Cite this

Bar-Noy, A., Peleg, D., Rabanca, G., & Vigan, I. (2015). Improved approximation algorithms for weighted 2-path partitions. In N. Bansal, & I. Finocchi (Eds.), Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings (pp. 953-964). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9294). Springer Verlag. https://doi.org/10.1007/978-3-662-48350-3_79

Bar-Noy, Amotz ; Peleg, David ; Rabanca, George et al. / Improved approximation algorithms for weighted 2-path partitions. Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. editor / Nikhil Bansal ; Irene Finocchi. Springer Verlag, 2015. pp. 953-964 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Improved approximation algorithms for weighted 2-path partitions",

abstract = "We investigate two NP-complete vertex partition problems on edge weighted complete graphs with 3k vertices. The first problem asks to partition the graph into k vertex disjoint paths of length 2 (referred to as 2-paths) such that the total weight of the paths is maximized. We present a cubic time approximation algorithm that computes a 2-path partition whose total weight is at least .5833 of the weight of an optimal partition; improving upon the (.5265 – ϵ)-approximation algorithm of [26]. Restricting the input graph to have edge weights in {0, 1}, we present a .75 approximation algorithm improving upon the .55-approximation algorithm of [16]. Combining this algorithm with a previously known approximation algorithm for the 3-Set Packing problem, we obtain a .6-approximation algorithm for the problem of partitioning a {0, 1}-edge-weighted graph into k vertex disjoint triangles of maximum total weight. The best known approximation algorithm for general weights achieves an approximation ratio of .5257 [4].",

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Bar-Noy, A, Peleg, D, Rabanca, G & Vigan, I 2015, Improved approximation algorithms for weighted 2-path partitions. in N Bansal & I Finocchi (eds), Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9294, Springer Verlag, pp. 953-964, 23rd European Symposium on Algorithms, ESA 2015, Patras, Greece, 14/09/15. https://doi.org/10.1007/978-3-662-48350-3_79

Improved approximation algorithms for weighted 2-path partitions. / Bar-Noy, Amotz; Peleg, David; Rabanca, George et al.
Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. ed. / Nikhil Bansal; Irene Finocchi. Springer Verlag, 2015. p. 953-964 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9294).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Bar-Noy A, Peleg D, Rabanca G, Vigan I. Improved approximation algorithms for weighted 2-path partitions. In Bansal N, Finocchi I, editors, Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. Springer Verlag. 2015. p. 953-964. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-48350-3_79

Improved approximation algorithms for weighted 2-path partitions

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